Of all the feelings about New Labour at the last election, it was hatred that was the most striking. It was the view of a minority but they were vocal, and it was the intensity of the emotion that made such an impact. Hatred is about betrayal. For some the betrayal was the Iraq war or civil liberties, and that has been powerfully articulated. But there was – and is – another account of betrayal in which a liberal elite, smugly superior in their metropolitan progressivism, championed globalisation and sold ordinary working people down the river.

This is not comfortable stuff. Too many elements of this story have some truth in them. And to compound the discomfort, it's a story that feeds into neuralgic arguments about multiculturalism. For both reasons, it's a betrayal that hasn't had the attention it deserves.

As Labour begins the local election campaign, there are plenty around the party wondering whether a year of coalition government has been enough to neutralise this loathing. Some are arguing that Labour just has to play its cards right, in contrast to a public-school dominated, public spending cuts government, for it to reassume the mantle of the working man and woman's champion.

Or maybe not. It may require a rather more rigorous and energetic soul-searching, argues a group of thinkers and politicians. They are alarmed at how New Labour strained and broke the historic alliance in the party between middle-class liberals and working-class communitarians, and ended up presiding over the loss of four million voters between 1997 and 2010.

Intent on that kind of soul searching are people such as Maurice Glasman, the political theorist who is now, thanks to Ed Miliband's peerage, introducing the House of Lords' terrace to the delights of roll-ups. A wonderfully eclectic thinker, Glasman, credited as the father of Blue Labour, confuses almost as much as he enlightens with his talk of Tudor statecraft. Closely connected to Glasman is Jonathan Rutherford, Miliband's old friend Marc Stears and that much respected political outrider Jon Cruddas. What they are talking about is like Marmite – some love it and some hate it. There are no policy prescriptions, that's not the point. But among their ideas are the raw materials from which Miliband could create a narrative – that much vaunted political necessity – with which to build renewal. Given how their ideas are creeping into his recent comments, it's obvious he's listening closely.

The central focus of the thinking is the emotional connection between party leadership and rank and file. The rationale is that it is just as important as the crucial issue of economic competence, if Labour is to rebuild trust. Miliband said last week that Labour is "your voice in tough times", but getting people to believe that is a very tall order, as much about empathy as economics.

The starting point is counter-intuitive: it is about the importance and value of nostalgia. In a remarkable speech in Liverpool last month, Cruddas acknowledged how "nostalgic" has been used as a term of contempt on the left for a generation; it's been belittled as backward and reactionary. Tony Blair said in 2004 "Leave the past to those who live in it", and repeatedly insisted on the inevitability of globalisation, the necessity of adapting to it and the virtues of modernisation; this was progress, he said.

It didn't feel like it to many people. In a time of massive change, inevitably there is much nostalgia, and for those who might be losing a lot, New Labour's orders, "Forward march", came across as bullying, authoritarian and inhumane. It also came across as self-interested; globalisation might serve the London middle classes well, but outside the south-east, where secure jobs were drying up and affordable housing was scarce, it had much less to offer. In the wake of the 2008 financial crisis, earlier anxieties about globalisation have been vindicated and reinforced; it has proved as volatile, disruptive and risky a process as many feared. "Arguably we are living through the most destructive period of capitalism since the 1930s. Is this progress?" asked Cruddas in his speech.

New Labour insisted it was. It brushed aside those who didn't agree as reactionary, and it urged adaptation and acceptance of change without recognition of the costs entailed in terms of relationships, communities and sense of place. David Miliband (who is also listening to this debate closely) signalled the necessary shift in his recent speech on the future of social democracy when he said: "We are not apologists for globalisation. We are reformers." It's a measure of how dire things had become, that this needed saying.

Nostalgia has to be recognised as legitimate; it's a powerful emotional current in the electorate with which politicians need to connect. Politics is fuelled as much by the desire to protect and preserve as it is by the ambition to change and reform. Nostalgia is not always passive, it can inspire resistance; indeed, Alastair Bonnett at Newcastle University argues in his book, Left in the Past, that nostalgia has fed a powerful radical tradition on the left that has resisted the disruptive force of industrialisation and the centralising power of the state. The force of nostalgia should be obvious right now, when leftwing politics are dominated by an urgent agenda of conservation of high-quality public services, the welfare state and the NHS.

It is the right wing that has traditionally been adept at understanding the value of nostalgia. The electorate needs recognition of valued traditions from their politicians, and will forgive them much else if such genuflections are offered. Margaret Thatcher managed to mask her radically disruptive politics with gestures to tradition; John Major and David Cameron have followed her model, if less skilfully.

What does a politics of nostalgia amount to? Cruddas, again, offers pointers: "People yearn for respect, belonging, identity, tradition. They yearn to fight against their insecurity." Jonathan Rutherford talks of a "conservative socialism". What they look back to are strands of early Labour thinking that shared much with Toryism – Romantic, popular, rooted in working-class experience of dispossession and English. But these strands fell by the wayside, marginalised by both liberalism, technocratic statism and internationalism.

They warn of how Labour talked too much of abstractions such as human rights; it gave too little space to the ordinary, the parochial, the routine, preferring instead to celebrate individual aspiration. What got lost was the community left behind and their collective languages of solidarity and security. This is what needs to be rehabilitated.

There is much that could go awry with these ideas. There's a lot of nervousness around the emphasis on Englishness because until now it's territory that has been left vacant for the far right to colonise (with the honourable early exception of Billy Bragg). Is there a way to redefine Englishness that allows for both nostalgia and multiculturalism?

Equally tricky is the question of what kind of credible economic policy nostalgia leaves room for? Neither are easy to answer. Nor is this a politics that is likely to go down well with a liberal London-based commentariat (and I include myself) who have a tin ear for much of this tricky emotional stuff. But how it feeds into the language, themes and stories Labour has to tell the country could be crucial in determining whether the party repeats its past pattern of defeat and faces several terms in opposition, or whether it manages to capitalise on rising opinion polls and bounce back.